We identify a feature of this setup which does not seem to have been considered explicitly to date: the loss itself may depend on our state of knowledge of the relation between parameters, for example, on \(\pi _0(\theta |\varphi )\) . This is present in the Gibbs posterior for the Cut model.
The Cut “posterior” for \((\varphi ,\theta )\)  is [1]}
\( {\tilde{p}}^{(c)}(\varphi ,\theta \mid Y, Z) = \pi (\varphi \mid Z) \pi (\theta \mid Y,\varphi ).\) 
